B

9000034906

Level: 
B
The solution set of one of the following quadratic inequalities is \(\left (-\infty ,-\frac{3} {5}\right )\cup \left (\frac{1} {6},\infty \right )\). Determine this inequality.
\(\left (5x + 3\right )\left (1 - 6x\right ) < 0\)
\(\left (5x - 3\right )\left (6x + 1\right ) < 0\)
\(\left (5x + 3\right )\left (1 - 6x\right ) > 0\)
\(\left (5x - 3\right )\left (6x + 1\right ) > 0\)

9000035005

Level: 
B
The railroad mound has the cross section of a isosceles trapezoid. The lengths of the bases are \(12\, \mathrm{m}\) and \(8\, \mathrm{m}\), the height is \(3\, \mathrm{m}\). Find the angle at the leg and round to the nearest degrees and minutes. See the picture with a isosceles trapezoid.
\(56^{\circ }19'\)
\(41^{\circ }45'\)
\(48^{\circ }11'\)
\(33^{\circ }69'\)

9000034907

Level: 
B
Find all \(x\in \mathbb{R}\) for which the following expression takes nonnegative values. \[ -2\left (x - 3\right )\left (2 - x\right ) \]
\(\left (-\infty ,2\right ] \cup \left [ 3,\infty \right )\)
\(\left [ 2,3\right ] \)
\(\left (2,3\right )\)
\(\left (-\infty ,2\right )\cup \left (3,\infty \right )\)

9000035006

Level: 
B
A ladder of the length \(15\, \mathrm{m}\) leans against a wall. The angle between the ladder and the horizontal direction is \(70^{\circ }\). Find the height of the top of the ladder and round your answer to the nearest meters.
\(14\, \mathrm{m}\)
\(13\, \mathrm{m}\)
\(16\, \mathrm{m}\)
\(15\, \mathrm{m}\)

9000034908

Level: 
B
Find all \(x\in \mathbb{R}\) for which the following expression is nonpositive. \[ \left (x + 1\right )\left (4 + x\right ) \]
\(\left [ -4,-1\right ] \)
\(\left (-\infty ,-4\right ] \cup \left [ -1,\infty \right )\)
\(\left (-4,-1\right )\)
\(\left (-\infty ,-4\right )\cup \left (-1,\infty \right )\)

9000035704

Level: 
B
Find the polar form of the complex number \( A \) graphed in the complex plane as shown in the picture.
\(z = 2\sqrt{2}\left (\cos \frac{3\pi } {4} + \mathrm{i}\sin \frac{3\pi } {4}\right )\)
\(z = 2\sqrt{2}\left (\cos \frac{\pi }{4} -\mathrm{i}\sin \frac{\pi }{4}\right )\)
\(z = 2\sqrt{2}\left (-\cos \frac{\pi }{4} + \mathrm{i}\sin \frac{\pi }{4}\right )\)
\(z = 2\sqrt{2}\left (\cos \frac{5\pi } {4} + \mathrm{i}\sin \frac{5\pi } {4}\right )\)

9000035601

Level: 
B
Find the values of the parameter \(p\in \mathbb{R}\) which guarantee that the following quadratic equation has solutions with nonzero imaginary part. \[ px^{2} - 3x + 4p = 0 \]
\(p\in \left (-\infty ,-\frac{3} {4}\right )\cup \left (\frac{3} {4},\infty \right )\)
\(p\in\left (-\frac{3} {4}, \frac{3} {4}\right )\)
\(p\in\left (\frac{3} {4},\infty \right )\)
\(p\in\left \{-\frac{3} {4}, \frac{3} {4}\right \}\)
\(p\in\mathbb{R}\setminus \left \{-\frac{3} {4}, \frac{3} {4}\right \}\)

9000035805

Level: 
B
Given the complex numbers \[ \text{$a = 2\left (\cos \frac{2\pi } {3} + \mathrm{i}\sin \frac{2\pi } {3}\right )$, $b = \sqrt{2}\left (\cos \frac{3\pi } {4} + \mathrm{i}\sin \frac{3\pi } {4}\right )$,} \] find the product \(ab\).
\(2\sqrt{2}\left (\cos \frac{17\pi } {12} + \mathrm{i}\sin \frac{17\pi } {12}\right )\)
\(2\sqrt{2}\left (\cos \frac{\pi }{2} + \mathrm{i}\sin \frac{\pi }{2}\right )\)
\(2\sqrt{2}\left (\cos \frac{5\pi } {7} + \mathrm{i}\sin \frac{5\pi } {7}\right )\)
\(2\sqrt{2}\left (\cos \frac{5\pi } {12} + \mathrm{i}\sin \frac{5\pi } {12}\right )\)

9000035806

Level: 
B
Given the complex numbers \[ \text{ $a = 2\left (\cos \frac{5\pi } {3} + \mathrm{i}\sin \frac{5\pi } {3}\right )$, $b = 3\left (\cos \frac{11\pi } {6} + \mathrm{i}\sin \frac{11\pi } {6} \right )$,} \] find the quotient \(\frac{a} {b}\).
\(\frac{2} {3}\left (\cos \frac{11\pi } {6} + \mathrm{i}\sin \frac{11\pi } {6} \right )\)
\(\frac{2} {3}\left (\cos \frac{\pi } {6} + \mathrm{i}\sin \frac{\pi } {6}\right )\)
\(\frac{2} {3}\left (\cos \frac{5\pi } {6} + \mathrm{i}\sin \frac{5\pi } {6}\right )\)
\(\frac{2} {3}\left (\cos \frac{7\pi } {6} + \mathrm{i}\sin \frac{7\pi } {6}\right )\)